Find the point on the line y 2x 1 which is closest to the

Find the point on the line y = 2x – 1 which is closest to the point (2, –1). Hint: Set up an appropriate distance function, then find its minimum value.

Solution

well you first can see that the line won\'t pass through the point (2, -1). So then you have to find a line that will connect (2, -1) to the line. The shortest path from the line to the (2, -1) is a perpendicular line. So the perpendicular line\'s equatiowell you first can see that the line won\'t pass through the point (2, -1). So then you have to find a line that will connect (2, -1) to the line. The shortest path from the line to the (2, -1) is a perpendicular line. So the perpendicular line\'s equation is y = -1/2x + b. Using the point slope formula, you can find out the equation to be y +1= -1/2 (x - 2) + b. So the final equation is y = -1/2x . Now you have to find the point in which the two lines intersect. since both equations have y, you can connect the two equations to get 2x - 1 = -1/2x . Then you just find the x value using algebra 5/2x = 1. x = 2/5 and y = -1/5. That\'s the point (2/5, -1/5).